Data-driven decision making under uncertainty integrating robust optimization with principal component analysis and kernel smoothing methods

This paper proposes a novel data-driven robust optimization framework that leverages the power of machine learning and big data analytics for decision-making under uncertainty. By applying principal component analysis to uncertainty data, correlations between uncertain parameters are effectively captured, and latent uncertainty sources are identified. These data are then projected onto each principal component to facilitate extracting distributional information of latent uncertainties using kernel density estimation techniques. To explicitly account for asymmetric distributions, we introduce forward and backward deviation vectors into the data-driven uncertainty set, which are further incorporated into novel data-driven static and adaptive robust optimization models. The proposed framework not only significantly ameliorates the conservatism of robust optimization, but also enjoys computational efficiency and wide-ranging applicability. Three applications on optimization under uncertainty, including model predictive control, batch production scheduling, and process network planning, are presented to demonstrate the applicability of the proposed framework.